Open Access
May, 1982 Edgeworth Expansions and Smoothness
P. J. Bickel, J. Robinson
Ann. Probab. 10(2): 500-503 (May, 1982). DOI: 10.1214/aop/1176993873


We give a necessary and sufficient condition for the distribution function of $n^{-1/2} \sum^n_{i=1} X_i$, where the $X_i$ are independently identically distributed with $EX_1 = 0, EX^2_1 = 1$ and $E|X_1|^{k+3} < \infty$, to possess an Edgeworth expansion to $k$ terms. The condition is not practicable but clarifies the relation between the existence of an Edgeworth expansion and the smoothness of the distribution function of the sum.


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P. J. Bickel. J. Robinson. "Edgeworth Expansions and Smoothness." Ann. Probab. 10 (2) 500 - 503, May, 1982.


Published: May, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0485.60018
MathSciNet: MR665604
Digital Object Identifier: 10.1214/aop/1176993873

Primary: 60F05

Keywords: central limit theorem , Edgeworth expansions

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 2 • May, 1982
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